If two stones are dropped from the same height, would the heavier stone hit the ground faster, slower or at the same speed? Why?
Let the two stones be dropped from a height h and have a mass M1 and M2.
The potential energy of the two stones at height h is M1*g*h and M2*g*h. As they fall the potential energy of the stones is converted to kinetic energy. Kinetic energy is given by (1/2)*m*v^2, where m is the mass and v is the velocity.
When the stone of mass M1 strikes the ground, its kinetic energy (1/2)*M1*v^2 = M1*g*h
=> v^2 = 2*g*h
=> v = sqrt (2*g*h)
Similarly for the stone with mass M2, the velocity is sqrt(2*g*h).
We see that the expression for velocity does not have the mass of the stone. This shows that the velocity of the stones when they strike the ground is the same and does not depend on the mass.